No abstract

for trapping as 6 decreases is reflective of the incorporation of periodic components into the sequence of numbers generated.To summarize the motivation and principal conclusion of this Letter, we restate' that for values of b where numerically generated sequences~P Pear to be chaotic, it has not been settled whether those sequences "are truly chaotic, or whether, in fact, they are really periodic, but with exceedingly large periods and very long transients required to settle down. " On the one hand, Grossman and Thomae" have suggested that (only) the parameter value b =1 generates pure chaos [see the discussion following Eq. (31) of Ref. 5 and the correlations plotted in their Fig. 9]. On the other hand, for certa, in other values of b, numberical results of Lorenz (reported in Ref. 1) "strongly suggest that the sequences are truly chaotic. " The purpose of this communication was to use an independent and exact result from the statistical-mechanical theory of d =1 random walks to test the randomness of the parabolic map for parameter values where the existence of "true chaos" is still an open question.Our results strongly support the conclusions of Grossmann and Thomae.Correlations of linear polarizations of pairs of photons have been measured with time-varying analyzers. The analyzer in each leg of the apparatus is an acousto-optical switch followed by two linear polarizers. The switches operate at incommensurate frequencies near 50 MHz. Each analyzer amounts to a polarizer which jumps between two orientations in a time short compared with the photon transit time. The results are in good agreement with quantum mechanical predictions but violate Bell's inequalities by 5 standard deviations.

When a neutral atom moves in a properly designed laser field, its center-of-mass motion may mimic the dynamics of a charged particle in a magnetic field, with the emergence of a Lorentz-like force. In this Colloquium we present the physical principles at the basis of this artificial (synthetic) magnetism and relate the corresponding Aharonov-Bohm phase to the Berry's phase that emerges when the atom follows adiabatically one of the dressed states of the atom-laser interaction. We also discuss some manifestations of artificial magnetism for a cold quantum gas, in particular in terms of vortex nucleation. We then generalise our analysis to the simulation of non-Abelian gauge potentials and present some striking consequences, such as the emergence of an effective spin-orbit coupling. We address both the case of bulk gases and discrete systems, where atoms are trapped in an optical lattice.